Conventional rare-earth sintered magnets containing fluorine-compounds are described in Japanese Patent Laid-Open No. 2003-282312. In the prior art, the fluorine-compound constitutes a granular grain boundary phase, and is not formed at the grain boundary or along the powder surface of the magnet. It does not disclose that a fluorine-containing layer is formed continuously and a further layer is in adjacent with the fluorine-containing layer, with an aim of reducing eddy current and ensuring energy product.